Cape not falling down in simulation
Yes, I do believe that you are correct in thinking that you need to up the steps of the simulation. You can find those in the cloth modifier tab under "Physics" in the Properties. 

Also, check if the hands and other body parts that need to collide have the collision in the "Physics" tab. More important, however, is proper subdivision. Make sure that the hand has proper subdivision and the cape is not only subdivided in one or two axis. For example make sure it looks like this: 

And not this: